Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory

@article{Naito2019ImprovementOF,
  title={Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory},
  author={Tomoya Naito and Daisuke Ohashi and Haozhao Liang},
  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
  year={2019}
}
We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn--Sham method and the density functional perturbation theory. Difference between the known EDF and the exact one is treated as the first-order perturbation. As benchmark calculations, we reproduce the theoretical exchange and correlation functionals in the local density approximation. Systems of noble-gas atoms are used for benchmark calculations, and the… 

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References

SHOWING 1-10 OF 173 REFERENCES
Exact Kohn-Sham scheme based on perturbation theory.
  • Görling, Lévy
  • Chemistry
    Physical review. A, Atomic, molecular, and optical physics
  • 1994
TLDR
An exact formal Kohn-Sham scheme is derived with the help of perturbation theory through the introduction of a basis set and an exact basis set ``exchange-only'' method is obtained.
Numerical methods for the inverse problem of density functional theory
The inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of
A long-range correction scheme for generalized-gradient-approximation exchange functionals
We propose a new long-range correction scheme that combines generalized-gradient-approximation (GGA) exchange functionals in density-functional theory (DFT) with the ab initio Hartree–Fock exchange
Density functional theory is straying from the path toward the exact functional
TLDR
The energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals, were found to become closer to the exact ones until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
Functional renormalization-group calculation of the equation of state of one-dimensional uniform matter inspired by the Hohenberg-Kohn theorem
We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) of an infinite nuclear matter (NM) in (1+1)-dimensions
Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms
Using accurate correlated wave functions calculated earlier by Bunge and by Larsson, we have constructed the Hohenberg-Kohn-Sham density functionals and exchange-correlation (ground-state) potentials
Exact Kohn-Sham Exchange Potential in Semiconductors
A new Kohn-Sham method that treats exchange interactions within density functional theory exactly is applied to Si, diamond, GaN, and InN. The exact local exchange potential leads to significantly
Density-functional exchange-energy approximation with correct asymptotic behavior.
  • Becke
  • Physics
    Physical review. A, General physics
  • 1988
TLDR
This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
...
...